# Bolt falls off rocket, find rocket acceleration

#### stangeroo

A rocket is launched straight up with constant acceleration. Four seconds after liftoff, a bolt falls off the side of the rocket. The bolt hits the ground 6.70 s later.

Find the rockets acceleration.

I dont understand how to set up this problem, ive never done something like this , asked some friends and they didnt know how to do it. Any help would be greatly appreciated

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#### Jameson

Work backwards kind of. If it took 6.7 for the bolt to hit the ground, how high was it?

$$d = v_{i}t + \frac{1}{2}at^2$$

vi = 0
a = -32 ft\sec^2 or -9.8 m\sec^2
t = 6.7 s

Solve for d.

Now, use the same equation and solve for "a" of the rocket.

$$d = v_{i}t + \frac{1}{2}at^2$$

d = part a
vi = 0
t = 4

Jameson

#### Doc Al

Mentor
Do it in two parts, but like this:
Part 1: Find the height and speed of the rocket after 4 seconds in terms of the rocket acceleration. Use:
$h = 1/2 a t^2$ and
$v = a t$

Part 2: Realize that the initial height and speed of the bolt equals the height and speed of the rocket after 4 seconds (which was calculated in part 1). The height of the bolt after it leaves the rocket is:
$h = h_0 + v_0t -(g/2)t^2$,
using $h_0$ and $v_0$ (in terms of a) from part 1; set h = 0 when t = 6.7 seconds. Solve for a.

thank you guys

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